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IMPRS lecture winter term 2001/02
Wednesday 10.15 am - 11.45 am
Reinhard Lipowsky and Ulrich Schwarz
Theory of soft and biomatter
This course provides an introduction to the theoretical concepts used
in soft matter
physics. Here soft matter means condensed matter which is characterized
by an
energy scale close to thermal energy, thus thermal noise is sufficient
to induce
configurational changes. This is true for all kinds of non-covalent
interactions
and includes material systems like colloids, polymers, fluid membranes
and
liquid crystals. It also includes biomatter, like vesicles and protein
networks, which
are a special focus of this course. We will start with the basic principles
from
thermodynamics and statistical mechanics. We then turn to lower-dimensional
objects (strings and interfaces), which determine the properties of
many soft matter
systems, and to their interaction with a physical environment. We introduce
the basic
concepts from elasticity theory and hydrodynamics, which often are
important
in soft matter physics, and finally discuss stochastic systems. Here
a special
focus will be molecular motors, which are responsible for directed
transport in biological
systems.
Contents:
1) 17.10.: Introduction and Overview
interdisciplinary research, role of thermal fluctuations and structure,
thermodynamics and
statistical mechanics, examples from own research (shape and elasticity
of droplets,
vesicles and cells, molecular motors, etc)
2) 24.10.: Classical thermodynamics and the 2nd law
equilibrium, state variables, entropy, heat flow, Sackur-Tetrode equation for ideal gas
31.10. no lecture (Reformationstag)
3) 7.11.: Principles of statistical thermodynamics
ensembles, entropy, Boltzmann factor, partition sum, fluctuation-dissipation
theorem,
thermodynamic limit, entropy as disorder
14.11. no lecture (J�lich Soft Matter Days)
4) 21.11.: Models for dilute systems
partition function for ideal gas, equations of state for ideal gas,
virial expansion, second
virial coefficient, important pair interaction potentials in colloidal
sciences
5) 28.11.: Phase transitions
second virial coefficient for van der Waals fluid, instability of van
der Waals equation of
state, Maxwell construction, first and second order phase transitions,
critical point,
spinoidal, hysteresis, Gibbs phase rule, phase diagrams for hard spheres
and Lennard-
Jones systems
6) 5.12.: Polymers as flexible strings
synthetic and biopolymers, Kuhn length, Gaussian chain, Gaussian propagator,
path
integral representation, ring polymer, polymer in box
7) 12.12.: Membranes as flexible surfaces
three deformation modes for thin shells, curvature energy for membranes,
role of
topology, Monge representation, thermal fluctuations, steric interaction,
membrane shapes
8) 19.12.: Interfaces under tension
surface tension, Laplace equation, surfaces of constant mean curvature,
minimal
surfaces, capillary waves, Rayleigh-Plateau instability, foams, wetting
morphologies,
Young equation
9) 9.1.: Adsorption, adhesion and wetting phenomena
polymers, membranes and interfaces in contact with walls, entropic interactions,
adsorption and unbinding transitions
10) 16.1.: Elasticity of soft material
strain and stress tensors, Hooke's law, Young modulus and Poisson ratio,
contact
mechanics, Hertz model, JKR-theory
11) 23.1.: Hydrodynamics
viscosity, Newtonian fluids, Navier-Stokes equation, Euler and Stokes
flow, shear and
Poiseuille flow, Stokes drag, life at low Reynolds-number
12) 30.1.: Brownian motion
diffusion and random walks, Markov processes, Fokker-Planck equation,
master
equations, Maxwell's demon
13) 6.2.: Molecular motors
cytoskeleton motors, two-state ratchet models, multiple-state ratchet
models
Recommended literature:
HE Callen, Thermodynamics and an introduction to thermostatistics,
Wiley, NY
F. Reif, Fundamentals of statistical and thermal physics, McGraw Hill, Boston
D Chandler, Introduction to modern statistical mechanics, Oxford University Press, NY
LE Reichl, A Modern course in statistical physics, Wiley, NY
H. Römer and T. Filk, Statistische Mechanik, VCH, Weinheim
R. Lipowsky and E. Sackmann, Eds., Structure and Dynamics of Membranes,
Elsevier, Amsterdam
PG de Gennes, Scaling concepts in polymer physics, Cornell University Press, Cornell
M Doi and SF Edwards, The theory of polymer dynamics, Clarendon Press, Oxford
H. Risken, The Fokker-Planck equation, Springer, Berlin
PM Chaikin and TC Lubensky, Principles of condensed matter physics,
Cambridge University Press, Cambridge
SA Safran, Statistical thermodynamics of surfaces, interfaces, and membranes,
Addison-Wesley, Reading
DF Evans and H Wennerström, The colloidal domain: where physics, chemistry,
and
biology meet, 2nd edition, Wiley 1998
